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Special Theory of Relativity Marc McGuigan North Quincy High School
Special Theory of Relativity
Marc McGuiganNorth Quincy High School
Outline
IntroductionRelativityThe speed of lightEinstein’s SolutionTime SpaceConclusion
IntroductionThe Special Theory of Relativity is the theory put forth by Albert Einstein in his 1905 paper, “On the Electrodynamics of Moving Bodies”“Special” because it applies the theory of relativity to inertial reference frames in flat space-time (no gravity)
Relative Motion
•Who is moving?
•How do we know?
•Up until Einstein we used addition and subtraction to calculate the observed speed to other objects
Relative Motion
Motion is relative as long as you are not accelerating!There is no experiment that you can do in an inertial reference frame that will distinguish it from another inertial reference frame
groundtraintrainobjectgroundobject vvv −−− +=
The Speed of Light
670 million miles per hour (in a vacuum)186,000 miles per secondLight always moves at the same speed You can never catch a beam of light!
Postulates of Special Relativity
1. “The laws of electrodynamics and optics will be valid for all frames of reference in which the laws of mechanics hold good (non-accelerating frames).”
2. “Light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body; here the velocity of light c is defined as the two-way velocity, determined with a single clock.”
Simultaneous EventsEvents that are simultaneous for observers in one reference frame are not necessarily simultaneous to observers in another reference frame
Time Dilation– Light Clock
What is time?What is a clock?
c = 3.0 x 108 m/s
Separation h = 15 cm
Period = Ts = 1 billionth of a second
mirror
mirror
h
Moving Light Clock
2mvT
2mvT
22
1 2⎟⎠⎞
⎜⎝⎛+= mvThL
•What happens if the light clock moves with a velocity v?
h2
22 2
⎟⎠⎞
⎜⎝⎛+= mvThL
The ball travels a distance:2
2
22 ⎟
⎠⎞
⎜⎝⎛+= m
TvThL
Time Dilation
c
vTh
cLT
m
Tm
22
22 ⎟
⎠⎞
⎜⎝⎛+
==
22
2vc
hTm−
= chTs
2=
Time Dilation
2
2
1cv
TT sm
−
=
2
2
1
1
cv
−
=γ
From one inertial reference frame it seems as though a clock moving in another frame ticks slower!
sm TT γ=
What about Length?
2
2
0 1cvLLm −=
Space-Time
We can think of 4 dimensions, three space and timeObjects move through space-time at the speed of light!If an object is “stationary” its motion is used to travel through timeIf the object “moves” in space, it travels more slowly through the time dimension
Relative Motion
21cvvvv
vgroundtraintrainobject
groundtraintrainobjectgroundobject
−−
−−−
+
+=
What happens if the velocity of the object with respect to the train is the speed of light?
cv groundobject =−
What is a Muon?
Semi-stable fundamental particleMuon mass is 207 times the mass of the electronDecays into a positron and two neutrinos
Evidence of Time Dilation - MuonsNon relativistic
Source: http://hyperphysics.phy-astr.gsu.edu/
Evidence of Time Dilation - MuonsRelativistic
Earth Frame
Source: http://hyperphysics.phy-astr.gsu.edu/
Evidence of Time Dilation - MuonRelativistic
Muon Frame
Source: http://hyperphysics.phy-astr.gsu.edu/
Twin ParadoxTwins – Earth Man and Rocket Man
Rocket Man takes off at a velocity 60 % of the speed of light
Rocket Man travel out 12 hours (by his watch) and then turns around and returns to Earth at the same speed that he left with.
When Rocket Man returns to Earth he has aged 24 hours.
How much has Earth Man Aged?
Answer: Earth Man has aged 30 hours!
E=mc2
2
20
1cv
mm−
=
2
2
202
1cv
cmmcE−
==
20cmErest =
4222 cmcpE +=20vmp γ=
The End
